Alita is just like a typical teenage girl. She loves chocolate, breaks curfew and crushes on a bad boy with floppy hair, a leather jacket and a motorcycle. But Alita isn’t typical in other ways. For one, she can slice apart a single falling tear with her ferocious battle sword.

Those are the two sides brought up by ”Alita: Battle Angel ,” our film entry into the thrilling manga world of artist Yukito Kishiro and imagined for the screen by producer James Cameron and director Robert Rodriguez. The film crams in so many plot lines that it risks being overstuffed but somehow stays true to its mesmerizing vision and emerges as a sci-fi success, if not a triumph.

Alita is both machine and human and the big-budget screen adaptation is both live action and computer generated, each element present in Alita herself, played with equal parts tenderness and ferocity by Rosa Salazar. She’s been given huge CG eyes but they’re not as distracting as you may fear. Somehow, Salazar still conveys deep emotion without a crucial acting tool. The film also has appearances by Jennifer Connelly, who is chilly and mysterious, and Mahershala Ali, who is chilly and dangerous.

The film begins with Alita’s torso found in a junk heap by a compassionate cyber-physician played by Christoph Waltz. The year is 2563 and we are in the crowded, chaotic streets of Iron City, a melting pot of survivors from a post-apocalyptic war. Cyborgs are everywhere and getting fresh parts seems to fuel the economy. (Curiously, plastic umbrellas are still in use. Cities can float in the sky here, but the population still relies on cheap plastic umbrellas.)

Alita’s human core is given a body and she awakens but has no memory of what came before. She must find out who she is and what her destiny is. “Whose rules do I live by?” she asks. Meanwhile, she falls for a human cyborg jacker (bland but hunky Keean Johnson) who has some moral issues to work out since he’s romancing a cyborg by day and slicing them apart at night.

There are several subplots involving cyberpunk bounty hunters, a ruling elite that lives in the sky and the town’s favorite sport — Motorball, a combination meth-fueled roller derby and Death Race. The film is rated PG-13 but there’s quite a bit of cyber-gore here, including gouging out eyeballs (more than once) and slicing metal folk in half or amputating them. If these were human, we’d be moving toward an R for sure.

The filmmakers are not afraid of making our heroine absolutely lethal and yet swooningly immature (she actually digs into her chest and offers her own artificial beating heart to her boyfriend, later laughingly admitting that gesture was “intense.”) She can give a beat-down to a roomful of hardened killers but still curl up on the couch and put her head on her adoptive dad’s chest. She can do flips worthy of an Olympic gymnast but her dad still wants her to wear knee pads and a helmet while competing at Motorball — against lasers, huge spinning saws and knives.

Alita has a strong moral compass — “I do not stand by in the presence of evil,” she announces — and, thankfully, triggering her special brand of martial arts mayhem must be earned. When a cute dog is senselessly slaughtered (relax, off camera), she dabs its blood on her face out of respect and revenge, squints really hard and coils up like lethal spring. It’s very clear whoever did that will not survive the next 5 minutes.

“Alita: Battle Angel,” which, in the end, needs more humor and less violence, kind of staggers quietly to its end. A sequel isn’t just hinted at — it’s practically dangled in front of our eyes as Alita looks heavenward to the next battlefield in the sky city. Well, count us in. Like Hailee Steinfeld in “Bumblebee,” Salazar’s Alita is part of a welcome wave of films about complex young women who know how to handle even the worst machines. Girls rule.

“Alita: Battle Angel,” a Twentieth Century Fox release, is rated PG-13 for “sequences of sci-fi violence and action, and for some language.” Running time: 122 minutes. Three stars out of four.

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MPAA Definition of PG-13: Parents strongly cautioned. Some material may be inappropriate for children under 13.